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and present address: C. R. Fonseca, Departamento de Biologia, CP. 275, Centro II, Universidade do Vale do Rio dos Sinos, São Leopoldo, RS, CEP. 93022-000, Brazil (email@example.com).
1The level of functional redundancy in natural communities is likely to modulate how ecosystem stability is affected by local species extinction. Thus, extinction should have no effect if all species have similar functions, but a major effect if each carries different functions.
2 We provide a probabilistic framework that, from any distribution of species number across functional groups, generates specific predictions of how functional groups are lost when species become randomly extinct within a given community. In particular, we predict how many species can go extinct before a community loses its first functional group, a useful index for conservation purposes.
3We demonstrate that the probability of a whole functional group becoming extinct from a given community increases with the number of recognized functional groups (functional richness) but decreases with species richness and functional evenness (the distribution of species across functional groups).
4 Application of this framework to one published data set for a South American plant community suggested that, if local extinction is random, 75% of the species could be lost before the disappearance of the first functional group.
5 However, if redundancy is to be used to determine conservation priorities, the definition of functional groups must be carefully reviewed.
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The importance of species diversity in controlling the stability of communities and ecosystems has been a focus of long-term debate (MacArthur 1955; Elton 1958; May 1972; Ehrlich & Ehrlich 1981; Walker 1992; Lawton & Brown 1993; Ehrlich & Walker 1998). It is widely accepted that continued species extinction invariably leads to irreversible degradation of ecosystem functions, including those involved in the maintenance of biogeochemical and hydrological cycles, climate control, decomposition and soil formation, pest control and pollination (Ehrlich & Ehrlich 1981). However, because species may play equivalent roles (i.e. are functionally redundant), some of them could go locally extinct without a substantial loss in ecosystem function (Walker 1992; Lawton & Brown 1993). The question is how much extinction can ecosystems support before they become unstable?
We examined how the stability of a natural ecosystem, built upon a wide range of ecological functions, will be affected by random species extinction. In particular, we predicted how functional groups are lost when species become randomly extinct from a given community and demonstrate how this probability is influenced by species richness, the number of functional groups (henceforth functional richness) and the distribution of species among functional groups (henceforth functional evenness).
The species–function extinction curve
We began by asking how many functional groups would be expected in a community when random extinction events have reduced its species richness. Assuming that the total number of species in the community is S, the total number of functional groups is F, and Si is the number of species in the functional
group . If random extinction events reduce
the species richness from S to s (S > s), then the expected number of functional groups in a random sample of s species [E(Fs)] will be given by:
where is the number of combinations of s species
that can be chosen from a set of S species (S!/s!(S − s)!). The mathematical solution of this estimate is analogous to that of the rarefaction method developed to allow comparisons of species diversity among samples with distinct sampling effort (Sanders 1968; reviewed by Hulbert 1971). The large sample variance of this estimate is that given by Heck et al. (1975) as
where Var(Fs) is the variance of the expected number of functional groups in a random sample of s species.
Some illustrative contrasts
We use equations (1) and (2) to compare four hypothetical communities showing independent variation in species richness (100 or 50 species), functional richness (20 or 10 functional groups) and functional evenness (with either a similar or a different number of species per functional group). Communities I and II differ in species richness but functional richness and evenness are held constant (Fig. 1a), whereas communities I and III differ only in functional evenness (Fig. 1c) and communities I and IV differ only in functional richness (Fig. 1e).
Because our model gives the expected number of functional groups for any number of species extinctions, comparisons among communities can be based on the whole curve relating species extinction to function losses. In addition, the curves allow us to ask how many functional groups are lost for any number of species extinctions, and how many species losses will lead to 10%, 50% or 90% of the functional groups being lost. In the following examples we restrict our comparisons of different communities to asking how many species extinctions can be supported before a community suffers the extinction of the first functional group. We believe that, for both ecologists and conservation biologists, this is a non-trivial question that is at the heart of the redundancy controversy (Ehrlich & Ehrlich 1981; Walker 1992; Lawton & Brown 1993; Ehrlich & Walker 1998).
The species richness contrast
Species-rich communities tend to have more functional redundancy than species-poor communities, at least when functional richness and functional evenness do not vary dramatically among communities. Quantitative evidence that richer communities will be less sensitive to extinction is given by comparison of the species–function extinction curves for communities I and II (Fig. 1b). In fact, the richer community I (100 species) is expected to support on average 80 random extinctions (80% of the species) before losing the first functional group, whereas community II (50 species) loses its first functional group after only 32 species (64%) have become extinct.
The functional evenness contrast
Communities exhibiting a more even distribution of species number across functional groups will present more functional redundancy than communities in which species are distributed unevenly among functional groups, others factors being equal. The quantitative comparison shows that community III, with an uneven distribution of species across functional groups, is able to withstand on average only 20 random species extinctions (20%) before it loses the first functional group, 60 fewer than observed for community I (Fig. 1d).
The functional richness contrast
Communities with fewer functional groups tend to have more functional redundancy than functionally rich communities. For example, community IV, with twice the number of functional groups of community I (20 and 10, respectively), is able to randomly lose on average 56 species (56%) before losing the first functional group, 24 fewer than in community I (Fig. 1f).
An empirical example
Although, in nature, species richness, functional richness and functional evenness are unlikely to change independent of each other, as in our hypothetical examples, the species–function extinction equation can be readily applied to any community in which the distribution of species across functional groups is known.
We therefore looked in the literature for empirical studies that classify all species from a community into functional groups based on their effect on the functioning of the ecosystem. Surprisingly, we were unable to find any empirical study that conformed strictly to such a definition, however, Díaz & Cabido (1997) used a hybrid definition, considering plant functional groups as sets of plants both exhibiting similar responses to environmental conditions and having similar effects on the dominant ecosystem processes. Despite the fact that some of the conclusions therefore need to be viewed more critically, we believe that this example can help us to understand some of the advantages and limitations of our approach.
In order to classify the 100 most abundant plant species along a steep climatic gradient in central-western Argentina into functional groups, Díaz & Cabido (1997) selected 24 key vegetative and regenerative traits. These were chosen to reflect the ecosystem functions (e.g. nutrient cycling, water retention, productivity, carbon storage) most likely to be modified by climatic change. Standard multivariate ordination and classification techniques (DCA and twinspan) were applied to the species × traits matrix, and eight functional groups have been identified: (FT1) short graminoids; (FT2) tussock grasses and large forbs; (FT3) short herbaceous and semi-woody erect, creeping or rosette-like dicots; (FT4) saxicolous or epiphytic rosettes; (FT5) trees; (FT6) evergreen shrubs and small trees; (FT7) aphyllous or scale-leafed shrubs; and (FT8) globular, cylindrical and columnar branched stem-succulents of various sizes.
The distribution of species across functional groups was relatively uneven (Fig. 2a), ranging from 29 species in FT1 to four in FT4 and FT7. Our model predicted that this community can support up to 75 random extinctions (75% of the original species number) before suffering the extinction of the first functional group (Fig. 2b).
The general analytical solution presented for the relationship between functional richness and species richness allows specific predictions about community and/or ecosystem stability. Here we are concerned with the extinction of whole functional groups within communities, rather than the relationship between function and species diversity within functional groups (as in Vitousek & Hooper 1993). We have shown that functional loss is more likely if communities are: (i) species poor, (ii) functionally rich, and (iii) have species distributed unevenly across functional groups.
Previous theoretical models have similarly suggested that species redundancy is important for the functioning and reliability of ecosystems (Naeem 1998) and our model further highlights that system stability and reliability depend on how species redundancy is distributed across functional groups. We were unable to find studies that classify whole communities into functional groups on the basis of their effect on a wide range of ecosystem processes (but see Walker et al. 1999). Data on such distributions, and thus of how species richness, functional richness and functional evenness are correlated with each other in nature, are thus fragmentary. For example, although one might imagine that, at least up to a given point, communities with more species (e.g. tropical forests) will tend to contain more functional groups than species-poor communities (e.g. boreal forests), this does not have to be the case.
There are several hypothetical ways in which species richness and functional richness can be associated in nature (Vitousek & Hooper 1993; Martinez 1996; Naeem 1998). As case studies accumulate, it is possible that there will be at least one empirical study to corroborate most of the hypothetical patterns, and a posteriori data analysis could then determine which hypothesis received the strongest support. Our model, however, allows us to make a priori quantitative predictions of the relationship between species and functional richness. The predicted species–function extinction curve provides both a null hypothesis against which observed data can be tested and the best means available to predict future changes in the absence of species- or functional group-specific information.
The deviation around the species–function extinction curve, in addition to its statistical relevance, has a very important biological meaning. As a rule, the variance in the expected number of functional groups tends to be low at either low or high species extinction levels, and to be high at intermediate species extinction levels (see Figs 1 and 2). When species become extinct at random, the first species to go extinct locally will, in most cases, have no effect on the functioning of the ecosystem, as their jobs will be taken by members of the same functional group. Similarly, when species extinction levels are high most redundant species will already have disappeared, and the extinction of any further species will be bound to produce an effect on the functioning of the ecosystem, and variance around our predictions will, therefore, be low. In contrast, when species extinction levels are intermediate, our certainty about the system behaviour is very low. In some cases, by chance, the community will retain at least one representative of each functional group and the system will continue to work, but if extinction events happen to have an impact on functional groups with no redundancy, ecosystem stability will be affected. In other words, if we lose one species we can confidently predict what should happen to the ecosystem but, if a few species are lost we can only guess. This unpredictability pattern of species extinction on ecosystem function was foreseen by Ehrlich & Ehrlich (1981).
Comparing redundancy levels
By deriving species–function extinction curves for different communities one is able to compare them in terms of functional redundancy. Although the curve can be compared, we envisage that the number of random extinctions the community supports (or the percentage that could become extinct) before it suffers the extinction of the first functional group represents a useful index of species redundancy across communities. Such indicators could allow the detection of which set of communities is more prone to functional extinction and therefore requires more intensive conservation efforts. A community that can lose up to 50% of its species before experiencing a functional loss is certainly more robust than a community that will lose the first functional group after 10% of its species become extinct.
The predictions of each species–function extinction curve are, however, valid only within the scope and definitions of the study concerned, and meaningful comparisons between communities or data sets require consistent definition and classification of species into functional groups.
The empirical prediction
Our model was able to produce specific a priori predictions about the plant community of central-western Argentina studied by Díaz & Cabido (1997), i.e. if local extinction is random, 75% of the species could go extinct before the disappearance of the first of the eight recognized functional groups. However, the high redundancy level thus suggested must be interpreted with caution, as classification procedures of species into functional groups strongly affect the estimated levels of redundancy in natural communities.
Redundancy and the definition of functional groups
One of the main assumptions of our model is that species can readily be classified into functional groups. Species are, however, evolutionarily and ecologically unique, and grouping into any functional classification will inevitably ignore some biologically relevant information. The exclusion of any species from a community is bound to have some effect, however marginal, on the functioning of the ecosystem. How much information will be included in the classification system and how much we are willing to neglect will depend on the aim and use in mind.
In any particular case, the definition of functional groups involves five main steps: (i) deciding which type of functional group is needed; (ii) selecting the criteria for including species in the study (e.g. all species in a forest patch); (iii) selecting which functions should be considered (e.g. nitrogen and carbon fixation); (iv) choosing morphological, physiological or ecological traits which reflect such functions (e.g. N-fixation ability, wood volume); (v) choosing and applying objective multivariate methods (e.g. cluster analysis) to the species–trait matrix (S species × T traits) thus produced. Choices to be made at each step will have consequences for the model predictions.
Defining functional group
Our focus on classifications that group species in relation to their effect on ecosystem processes (Walker 1992) works well under relatively stable environmental conditions. However, if the local environment drifts due to external environmental pressure (e.g. global change), heterogeneity can emerge within apparently homogeneous functional groups, because species that apparently do the same thing can respond quite differently to environmental pressures. Although Walker et al. (1999) argue that this heterogeneity is good as it increases the system’s resilience to environmental changes, it may lead to redundancy levels being dangerously overestimated. Actual levels of functional redundancy can be estimated more accurately when functional group is defined as a set of species exhibiting similar responses to environmental conditions and having similar effects on the dominant ecosystem processes (Díaz & Cabido 1997).
Although most present-day global change research is aimed at understanding shifts in species’ geographical range (Smith et al. 1997), prediction of ecosystem-level functions of the new, post-disturbance community composition is also important and may be better founded on Díaz & Cabido’s (1997) definition than based strictly on the response of species to disturbance.
Species inclusion criteria
Most community studies have at least a taxonomic and a spatial criterion for species inclusion, and the latter is particularly relevant for the redundancy controversy. Because communities are defined operationally as the set of species in a given area at a given time, and more area normally means more species (MacArthur & Wilson 1967), it is inevitable that redundancy is scale dependent. Local communities thus have less redundancy than regional, or larger scale, communities but the spatial structure of vegetation means that, at the larger scale, two species with similar function should be regarded as redundant only if they co-occur. For example, all trees were considered to be part of the same functional group in Díaz & Cabido’s (1997) study, but two trees should not be considered as functionally equivalent if they occur in two different parts of the environmental gradient.
Selecting the functions of interest
If only a few functions are considered in the study, then the level of functional redundancy will be very high; the addition of more functions will increase the probability of a species having a unique role, therefore decreasing the redundancy level accordingly. If species redundancy is discussed only in terms of major ecosystem processes, such as carbon fixation, nutrient cycles and water retention, it is conceivable that a dozen plant species will be sufficient to fulfil all roles. For the functional group definition to become more complete and useful, ‘dominant ecosystem processes’ should be understood as including both: (i) the flow of energy and materials (nutrients, water, atmospheric gases) in the system; and (ii) community and population processes normally found in an integral community (e.g. pollination, dispersal, herbivory).
Choosing the traits
After selecting the functions of interest, it is necessary to find species traits that reflect them. This task is not an easy one because the relationship between form and function is hardly straightforward and is limited further by practical considerations of which traits can be screened for a large set of species. Functional groups built for different purposes therefore tend to be based on a similar range of traits (see Leishman & Westoby 1992; Díaz & Cabido 1997).
Building a classification
The question of how to choose a single multivariate method to classify species into groups among the range of alternatives (e.g. cluster analysis, DCA, twinspan) is itself not trivial, but all suffer from a similar problem, illustrated here for hierarchical arrangements of species into groups of decreasing similarity produced by cluster analyses. At one extreme, all species could be considered to be part of a single functional group, whereas if enough traits are considered, each species will constitute a ‘functional group’ by its own. It is therefore up to the researcher and the methodology to adopt an appropriate ‘cut-off’ level defining how much trait variation we are willing to overlook in order to give workable functional groups, and thus how much dissimilarity will be allowed within each group. The literature suggests that high cut-off levels are frequently accepted (e.g. Leishman & Westoby 1992; Boutin & Keddy 1993; Golluscio & Sala 1993; Díaz & Cabido 1997), producing functional groups that can be easily recognized (e.g. growth forms) but encompassing high levels of trait variation (i.e. all trees are assumed to function in the same way). By doing so, functional redundancy inevitably emerges as very high, as in our empirical example using the Díaz & Cabido (1997) data set. Functional groups produced with lower cut-off levels will increase the homogeneity of functional groups and, consequently, define lower redundancy levels.
In summary, we would like to highlight that if conservation priorities or programmes of management or ecosystem restoration are to be based on functional redundancy, as proposed by Walker (1992), the best definition of functional group for the conservation aim in question must be sought and, in order to be conservative, this may need to use as many functional groups as possible.
Another main assumption of our model is that local species extinction is considered to occur at random, with the probability of extinction being equally distributed across species and functional groups. The basic model could be further improved by the incorporation of differential extinction probabilities across species and functional groups. Empirical research is needed to determine if and how: (i) extinction of whole functional groups modifies the extinction probabilities of those remaining because of interactions among different functions; and (ii) the extinction of individual species affects others in the same functional group due, for instance, to compensatory effects (Naeem 1998). Future theoretical work could include species-specific information on differences in mating system, local population density and geographical range that can modulate species extinction and thus predict more accurately the extinction rates of functional groups. Such models would be of great value for conservation programmes of functionally complex systems.
We thank Michelle Leishman, David Warton, Thomas Lewinsohn, Lindsay Haddon and the BIOFORUM discussion group for suggestions in earlier versions. The authors were supported by CNPq, FAPERJ and FAPESP (Brazil). This work is part of the BIOTA/FAPESP – The Biodiversity Virtual Institute Program (http://www.biotasp.org.br).
Received 19 November 1999 revision accepted 5 October 2000